DTNO: Direct-Time Neural Operators for One-Pass Spatiotemporal Forecasting

Autoregressive neural PDE surrogates advance a system one or a few steps at a time, causing inference cost to grow with forecast horizon and allowing prediction errors to accumulate through repeated feedback. We study the Direct-Time Neural Operator (DTNO), a finite-time neural operator that predicts a requested future state in a single network evaluation. DTNO decomposes forecasting into a horizon-independent encoder, a lead-time-conditioned latent evolution operator, and a residual decoder. Lead time modulates the Fourier operator blocks through feature-wise linear modulation, enabling a single model to predict across multiple forecast horizons without autoregressive rollout. We evaluate DTNO on five spatiotemporal systems ranging from reaction-diffusion dynamics to reacting flows, using a common FNO backbone, matched training splits, and the same evaluation protocol as an autoregressive counterpart. For a requested future state, DTNO uses a single forward pass rather than a number of rollout steps that grows with the forecast horizon. Across these systems, autoregressive forecasting is more accurate at short lead times, whereas DTNO consistently achieves superior accuracy at medium horizons, with accuracy transition points emerging between \(h=8.1\) and \(h=19.1\). At \(h=32\), DTNO achieves lower relative \(L_2\) field error than the matched autoregressive baseline on all five datasets, while eliminating recursive error feedback and requiring no sequential rollout between the observed state and the queried horizon. DTNO also exhibits substantially lower variation across repeated training runs. These results show that direct finite-time prediction provides a practical alternative to autoregressive rollout for medium- and long-horizon spatiotemporal forecasting. By conditioning a shared neural operator directly on forecast time, DTNO combines horizon-flexible prediction, constant-depth inference, and improved long-horizon stability within a single model.